Performance Evaluation of parallel Computers

1. PERFORMANCE
EVALUATION OF
PARALLEL COMPUTERS
CSE539
(Advanced Computer Architecture)
Sumit Mittu
(Assistant Professor, CSE/IT)
Lovely Professional University

2. BASICS OF
PERFORMANCE EVALUATION
A sequential algorithm is evaluated in terms of its execution time which is
expressed as a function of its input size.
For a parallel algorithm, the execution time depends not only on input size but also
on factors such as parallel architecture, no. of processors, etc.
Performance Metrics
Parallel Run Time
Speedup
Efficiency
Standard Performance Measures
Peak Performance
Sustained Performance
Instruction Execution Rate (in MIPS)
Floating Point Capability (in MFLOPS)
2

3. PERFORMANCE METRICS
Parallel Runtime
The parallel run time T(n) of a program or application is the time required to run
the program on an n-processor parallel computer.
When n = 1, T(1) denotes sequential runtime of the program on single processor.
Speedup
Speedup S(n) is defined as the ratio of time taken to run a program on a single
processor to the time taken to run the program on a parallel computer with
identical processors
It measures how faster the program runs on a parallel computer rather than on a
single processor.
3

4. PERFORMANCE METRICS
Efficiency
The Efficiency E(n) of a program on n processors is defined as the ratio of
speedup achieved and the number of processor used to achieve it.
Relationship between Execution Time, Speedup and Efficiency and the
number of processors used is depicted using the graphs in next slides.
In the ideal case:
Speedup is expected to be linear i.e. it grows linearly with the number of
processors, but in most cases it falls due to parallel overhead.
4

5. PERFORMANCE METRICS
Graphs showing relationship b/w T(n) and no. of processors
<<<IMAGES>>>
5

6. PERFORMANCE METRICS
Graphs showing relationship b/w S(n) and no. of processors
<<<IMAGES>>>
6

7. PERFORMANCE METRICS
Graphs showing relationship b/w E(n) and no. of processors
<<<IMAGES>>>
7

8. PERFORMANCE MEASURES
Standard Performance Measures
Most of the standard measures adopted by the industry to compare the
performance of various parallel computers are based on the concepts of:
Peak Performance
[Theoretical maximum based on best possible utilization of all resources]
Sustained Performance
[based on running application-oriented benchmarks]
Generally measured in units of:
MIPS [to reflect instruction execution rate]
MFLOPS [to reflect the floating-point capability]
8

9. PERFORMANCE MEASURES
Benchmarks
Benchmarks are a set of programs of program fragments used to compare the
performance of various machines.
Machines are exposed to these benchmark tests and tested for performance.
When it is not possible to test the applications of different machines, then the
results of benchmark programs that most resemble the applications run on those
machines are used to evaluate the performance of machine.
9

10. PERFORMANCE MEASURES
Benchmarks
Kernel Benchmarks
[Program fragments which are extracted from real programs]
[Heavily used core and responsible for most execution time]
Synthetic Benchmarks
[Small programs created especially for benchmarking purposes]
[These benchmarks do not perform any useful computation]
EXAMPLES
LINPACK
LAPACK
Livermore Loops SPECmarks
NAS Parallel Benchmarks Perfect Club Parallel Benchmarks
10

11. PARALLEL OVERHEAD
Sources of Parallel Overhead
Parallel computers in practice do not achieve linear speedup or an efficiency of 1
because of parallel overhead. The major sources of which could be:
•Inter-processor Communication
•Load Imbalance
•Inter-Task Dependency
•Extra Computation
•Parallel Balance Point
11

12. SPEEDUP
PERFORMANCE LAWS
Speedup Performance Laws
Amdahl’s Law
[based on fixed problem size or fixed work load]
Gustafson’s Law
[for scaled problems, where problem size increases with machine size
i.e. the number of processors]
Sun & Ni’s Law
[applied to scaled problems bounded by memory capacity]
12

13. SPEEDUP
PERFORMANCE LAWS
Amdahl’s Law (1967)
For a given problem size, the speedup does not increase linearly as the number of
processors increases. In fact, the speedup tends to become saturated.
This is a consequence of Amdahl’s Law.
According to Amdahl’s Law, a program contains two types of operations:
Completely sequential
Completely parallel
Let, the time Ts taken to perform sequential operations be a fraction α (0<α≤1) of
the total execution time T(1) of the program, then the time Tp to perform parallel
operations shall be (1-α) of T(1)
13

14. SPEEDUP
PERFORMANCE LAWS
Amdahl’s Law
Thus, Ts = α.T(1) and Tp = (1-α).T(1)
Assuming that the parallel operations achieve linear speedup
(i.e. these operations use 1/n of the time taken to perform on each processor), then
T(n) = Ts + Tp/n =
Thus, the speedup with n processors will be:
14

15. SPEEDUP
PERFORMANCE LAWS
Amdahl’s Law
Sequential operations will tend to dominate the speedup as n becomes very large.
As n  ∞, S(n)  1/α
This means, no matter how many processors are employed, the speedup in
this problem is limited to 1/ α.
This is known as sequential bottleneck of the problem.
Note: Sequential bottleneck cannot be removed just by increasing the no. of processors.
15

16. SPEEDUP
PERFORMANCE LAWS
Amdahl’s Law
A major shortcoming in applying the Amdahl’s Law: (is its own characteristic)
The total work load or the problem size is fixed
Thus, execution time decreases with increasing no. of processors
Thus, a successful method of overcoming this shortcoming is to increase the problem size!
16

17. SPEEDUP
PERFORMANCE LAWS
Amdahl’s Law
<<<GRAPH>>>
17

18. SPEEDUP
PERFORMANCE LAWS
Gustafson’s Law (1988)
It relaxed the restriction of fixed size of the problem and used the notion of fixed
execution time for getting over the sequential bottleneck.
According to Gustafson’s Law,
If the number of parallel operations in the problem is increased (or scaled up) sufficiently,
Then sequential operations will no longer be a bottleneck.
In accuracy-critical applications, it is desirable to solve the largest problem size on a
larger machine rather than solving a smaller problem on a smaller machine, with
almost the same execution time.
18

19. SPEEDUP
PERFORMANCE LAWS
Gustafson’s Law
As the machine size increases, the work load (or problem size) is also increased so
as to keep the fixed execution time for the problem.
Let, Ts be the constant time tank to perform sequential operations; and
Tp(n,W) be the time taken to perform parallel operation of problem size or
workload W using n processors;
Then the speedup with n processors is:
19

20. SPEEDUP
PERFORMANCE LAWS
Gustafson’s Law
<<<IMAGES>>>
20

21. SPEEDUP
PERFORMANCE LAWS
Gustafson’s Law
Assuming that parallel operations achieve a linear speedup
(i.e. these operations take 1/n of the time to perform on one processor)
Then, Tp(1,W) = n. Tp(n,W)
Let α be the fraction of sequential work load in problem, i.e.
Then the speedup can be expressed as : with n processors is:
21

22. SPEEDUP
PERFORMANCE LAWS
Sun & Ni’s Law (1993)
This law defines a memory bounded speedup model which generalizes both Amdahl’s Law
and Gustafson’s Law to maximize the use of both processor and memory capacities.
The idea is to solve maximum possible size of problem, limited by memory capacity
This inherently demands an increased or scaled work load,
providing higher speedup,
Higher efficiency, and
Better resource (processor & memory) utilization
But may result in slight increase in execution time to achieve this scalable
speedup performance!
22

23. SPEEDUP
PERFORMANCE LAWS
Sun & Ni’s Law
According to this law, the speedup S*(n) in the performance can be defined by:
Assumptions made while deriving the above expression:
•A global address space is formed from all individual memory spaces i.e. there is a
distributed shared memory space
•All available memory capacity of used up for solving the scaled problem.
23

24. SPEEDUP
PERFORMANCE LAWS
Sun & Ni’s Law
Special Cases:
•G(n) = 1
Corresponds to where we have fixed problem size i.e. Amdahl’s Law
•G(n) = n
Corresponds to where the work load increases n times when memory is increased n
times, i.e. for scaled problem or Gustafson’s Law
•G(n) ≥ n
Corresponds to where computational workload (time) increases faster than memory
requirement.
Comparing speedup factors S*(n), S’(n) and S’(n), we shall find S*(n) ≥ S’(n) ≥ S(n)
24

25. SPEEDUP
PERFORMANCE LAWS
Sun & Ni’s Law
<<<IMAGES>>>
25

26. SCALABILITY METRIC
Scalability
– Increasing the no. of processors decreases the efficiency!
+ Increasing the amount of computation per processor, increases the efficiency!
To keep the efficiency fixed, both the size of problem and the no. of processors must be increased
simultaneously.
A parallel computing system is said to be scalable if its efficiency can be
fixed by simultaneously increasing the machine size and the problem size.
Scalability of a parallel system is the measure of its capacity to increase speedup in proportion to
the machine size.
26

27. SCALABILITY METRIC
Isoefficiency Function
The isoefficiency function can be used to measure scalability of the parallel computing
systems.
It shows how the size of problem must grow as a function of the number of processors used in order to
maintain some constant efficiency.
The general form of the function is derived using an equivalent definition of efficiency
as follows:
Where, U is the time taken to do the useful computation (essential work), and
O is the parallel overhead. (Note: O is zero for sequential execution).
27

28. SCALABILITY METRIC
Isoefficiency Function
If the efficiency is fixed at some constant value K then
Where, K’ is a constant for fixed efficiency K.
This function is known as the isoefficiency function of parallel computing system.
A small isoefficiency function means that small increments in the problem size (U), are sufficient
for efficient utilization of an increasing no. of processors, indicating high scalability.
A large isoeffcicnecy function indicates a poorly scalable system.
28

29. SCALABILITY METRIC
Isoefficiency Function
29

30. PERFORMANCE
MEASUREMENT TOOLS
Performance Analysis
Search Based Tools
Visualization
Utilization Displays
[Processor (utilization) count, Utilization Summary, Gantt charts, Concurrency Profile, Kiviat
Diagrams]
Communication Displays
[Message Queues, Communication Matrix, Communication Traffic, Hypercube]
Task Displays
[Task Gantt, Task Summary]
30

31. PERFORMANCE
MEASUREMENT TOOLS
31

32. PERFORMANCE
MEASUREMENT TOOLS
32

33. PERFORMANCE
MEASUREMENT TOOLS
33

34. PERFORMANCE
MEASUREMENT TOOLS
34

35. PERFORMANCE
MEASUREMENT TOOLS
35

36. PERFORMANCE
MEASUREMENT TOOLS
Instrumentation
A way to collect data about an application is to instrument the application executable
so that when it executes, it generates the required information as a side-effect.
Ways to do instrumentation:
By inserting it into the application source code directly, or
By placing it into the runtime libraries, or
By modifying the linked executable, etc.
Doing this, some perturbation of the application program will occur
(i.e. intrusion problem)
36

37. PERFORMANCE
MEASUREMENT TOOLS
Instrumentation
Intrusion includes both:
Direct contention for resources (e.g. CPU, memory, communication links, etc.)
Secondary interference with resources (e.g. interaction with cache replacements or virtual
memory, etc.)
To address such effects, you may adopt the following approaches:
Realizing that intrusion affects measurement, treat the resulting data as an
approximation
Leave the added instrumentation in the final implementation.
Try to minimize the intrusion.
Quantify the intrusion and compensate for it!
37